Electrooptical function synthesizer



Fab, i5 119% HENRkGEQRGES DQLL MWMZ ELECTROOPTICAL FUNCTION SYN'Ii-XESIZER Filed 00$; 19, 1943 e Sheets-Sheet 1 INVENTOR. flfwwz- 623E663 30A 4 ATTOHZYE'YJ I Feb 7,, H5 HENRl-GEORGES DOLL. 9 3

ELECTROOPTICAL FUNCTiON SYNTHESIZER Filed. Oct. 19, 1943 6 Sheets-Sheet 2 Feb '1' 19% HENRI-GEORGES mm.:

ELECTROOPTICAL FUNCTION SYNTHESIZER Filed Oct. 19, 1943 6 Sheets-Sheet 3 9 5m HENRl-GEQRGES DOLL 2,497,42

ELECTROOPTICAL FUNCTION SYNTHESIZER Filed Oct. 19, 1945 6 Sheets-Sheet 4 w Q Q \Q ks m -%il I et mwmw Mm Feb, 7, 11950 HENRHGEORGES DOLL 2,497,042

ELECTROOPTICAL FUNCTION SYNTHESIZER Filed Oct. 19, 1943 6 Sheets-Sheet 5 m ATTQZPA/EKS Feb. 7 E959 HENRI-GEORGES DOLL 2,497,042

ELECTROOPTICAL FUNCTION SYNTHESIZER INVENTOR. I /EN/FI GL'ORGESZDOLL M WW v A TTOEJVEYJ Patented Feb. 7, 1950 2,497,042 ELECTROOPTICAL FUNCTION SYNTHESIZER Henri-Georges Electro-Mechanical 3 Claims.

The present invention relates to mathematical solvers and more particularly to new and improved apparatus for providing instantaneous solutions for values of a function of a plurality of variables where the instantaneous values of the variables are known.

Heretofore mechanical solving apparatus has been employed for this purpose. In such apparatus, a large number of moving mechanical parts such as gears, levers and cams, for example, are usually employed for performing desired mathematical operations on the variables involved in the function whose value is to be obtained. Since mechanical elements of this sort have mass, they introduce inertia effects which produce an undesirable time lag between the introduction of the values of the variables into the solver and the reaching of a solution. Also, such elements must be made to a high degree of precision to avoid back-lash and other mechanical difficulties that might introduce errors into the solutions obtained.

It is an object of the present invention, ac-

cordingly, to provide a new and improved mathe-- matical solver which is free from the above noted defects of the prior art.

Another object of the invention is to provide a new and improved solver in which few or no moving mechanical parts are employed for performing mathematical operations on the variables involved in the function whose value is to be obtained.

A further object of the invention is to provide a new and improved solver which receives electrical values proportional to the variables involved in the function whose value is to be determined, and provides instantaneous electrical values proportional to the values of said function.

A still further object of the invention is to provide a new and improved solver which is accurate, light in weight, and instantaneous in operation.

Still another object of the invention is to provide a new and improved solver of the above character which is capable of solving for negative and positive values of the function whose value is to be determined. Y

Broadly speaking, the objects of the invention are attained by modifying the intensity of a beam of radiant energy in accordance with instanta neous values of the variables on which the function depends, and directing the modified beam to a photosensitive device which provides an electrical output proportional to the instantaneous value of the function.

Doll, Houston, Tex., assignor to Research Incorporated. Ridgefield, Conn, a corporation of Connecticut Application October 19, 1943, Serial No. 506,827

The modification of the intensity of the beam 56 may be accomplished in a number of different" ways. For example, the beam may be transmitted through a screen laid out as a two-variable coordinate system, the radiant energy transmis-l sion coeiiicient of which at each point is proportional to the value of the function corresponding to the values of the variables at that point. If the beam is displaced parallel to the screen axes, proportionally to the instantaneous values of the respective variables, it is clear that the intensity of the radiant energy impinging on the photo-' sensitive device at any instant will be proportional to the value of the function corresponding to the instantaneous values of the variables at that instant.

A moving radiant energy beam of the desired.

character may be obtained according to the invention by directing radiant energy to a reflect ing surface which is rotated about an axis in accordance with values of one of the variables, and directing the reflected light to a second reflecting surface which is rotated, in accordance with values of a second variable, about an axis at right angles to the axis of the first reflecting member.

In another embodiment of the invention, electrical values proportional to the instantaneous values of two variables may be applied to the horizontal and vertical deflecting plates, respectively, of a cathode ray oscilloscope. The trace on the oscilloscope screen provides a beam of radiant energy of desired characteristics. Other devices, such as a Farnsworth dissector tube or a television tube of the type known as an iconoscope, may

, also be used for this purpose, as described in greater detail hereinafter.

A function of three variables may be solved by further modifying the radiant energy beam in accordance with values of the third variable. Functions of four or more variables may "also be solved according to the invention by employing a plurality of solvers and supplying the output of one solver as one of the variable inputs 'to a second solver.

The invention may be better understood from the following detailed description of several representative embodiments, takengyin conjunction with the accompanying drawings, in which:

Figure 1 illustrates *sfliematically solving apparatus constructed according to the invention; Figures 2, 3, 4 and 5 illustrate different types of screens corresponding to different types of functions that may besolved with the apparatus shown in Figure 1; t

Figures 6 and 7 areschmatlcdiusrams of cir-,

cuits enabling solutions of proper sign to be obtained for both positive and negative functions;

Figure 8 illustrates schematically another embodiment of the invention which utilizes a cathode ray oscilloscope;

Figure 9 illustrates schematically a further embodiment employing an iconoscope; and

Figure illustrates schematically a still further embodiment utilizing a Farnsworth dissector tube.

In the embodiment illustrated in Figure 1 of the drawings, a beam of radiant energy is displaced in two mutually perpendicular directions by a combination of reflecting surfaces having mutually perpendicular axes-of rotation.

Referring to Figure l, the solving apparatus comprises a pair of reflecting surfaces 10 and H such as small mirrors, for example, which are mounted for rotation about the mutually perpendicular axes :r--r and yg respectively, in accordance with magnitudes of the variables x and y. To this end, the mirrors l0 and H may bedirectly connected to 'mechanical elements whose displacements represent magnitudes of the variables x and y, or they may be attached to the moving coils of two galvanometers G1 and G2 which are energized by'electrical currents proportional to the magnitudes of the variables at and y, respectively, as shown. A light beam [2 is provided by a suitable light source I3 and is directed by means of a conventional type lens l4 upon the mirror'lll from which it'is reflected to the mirror I I and reflected from the latter to a screen 15, upon which the light beam is focused. "Disposed in'the path of the beam reflected from the mirror II is a screen [5, to be described hereinafter, which modifies the intensity of the light in accordance with the magnitudes of the variables x and y. The modified light beam is focused by means of a conventional type lens l6 upon a conventionaltype photosensitive element H which may be a photoelectric cell, for example. Ifa light beam of constant intensity is employed, the photoelectric cell I! should preferably be shielded to prevent stray light from reaching it, and a conventionaltype direct ourrent'amplifiershould be provided 'for amplifying its output. It is more convenient, however; to modulate'the light beam by applying alternating current to'the source 13, or by placing an interrupter G in the path of the beam l2, for example. Where this is done, a conventional alternating current amplifienmay' be provided for the photoelectric cell [1, as described below.

'The electrodes l3 and'l9 of the photoelectric cell E! are connected to the plate electrode 20 and the control grid electrode 2|, respectively, of a conventional type electronic amplifying tube 22. The plate el'ectrode20 of the tube 22 and the anode [8 of the photoelectric cell i! are both supplied with electrical energy from a suitable source 23. Grid bias for the electronic tube 22 is provided by a potentiometer comprising a sourceof' voltage 24 and a resistor 25, the variable contact 26 of which is connected to the control grid 2! of thetube 22 through a resistance 26a.

In the plate circuit of the tube 22 is connected the primary winding '21 of a transformer 28, the secondary winding 29 of which is connected to the anodes 38 and 3|,respectively, of the rectifying tubes 32 and 33, respectively. The output of the rectifiers 32 and '32) is impressed across a load resistance 34, which is connected at one end. to the mid-tap 35- ofthe transformer secondary winding 29 and at its other end to the filaments 36' and -31-of the rectifiers 32 and -33,

respectively. The resistance 34 can be shunted advantageously by means of a condenser to reduce the A. C. component (principally second harmonic) of the rectified current.

The screen [5 is provided with a horizontal axis 32-1: and a vertical axis yy, as shown, and its transparency at each point of the coordinate system is such that the amount of light transmitted at that particular point is directly proportional to the function z=f(:r, y)for which solutions are to be made.

In operation, the mirrors l0 and I i are adjusted so that when the magnitudes of the variables a: and' y are both zerofthe light beam l2 passes through the origin 0 of the r-m, yy coordinate system. If the mirrors [0 and II are then rotated about their respective axes in accordance with the magnitudes of the variables x and 11. respectively, for any given values we and yo of the variables the light beam I2 will impinge upon the screen' I 5'at the corresponding point (:ro, yo), and the a'riiou' nt of light reaching the photoelectric cell i! will'be directly proportional to the value of thel'u'nction a corresponding to those particular values of the variables a: and y. The electrical output of the solver is received by a device 'D' which may be a suitably calibrated indicator or a devicetobe actuated in accordance with values of the function solved for.

When a modulated light beam isused in order to p'ermit'the useof alternating current amplifiers,'the output gives the average instantaneous value of'the function e.

Representative"screens corresponding to a number of simple wen known functions of two variables are'shown in Figures 2-5, inclusive. Figure 2 illustrates ascre'en representing the funtion a ry. The screens in Figures 3, 4 and 5 correspond to the functions is 'desired.

Frommany applications, however, it is sufllcient todetermine'the instantaneous value of the function z=f(a:, only approximately. In some instances, an accuracy of plus or minus 5 or-l0%maybe entirely-adequate. In such cases, the transparency of the screen need not be determined to any greater degree-ofac'curacy, and a satisfactoryscreeamay be constructed by dividing-its" surface into different zones varying progressively in trar'isparency by 5 or 10%, for ex-' ample. ,For screens of-this type it is necessary onlyto calculate the lines of equal transparency which constitute the-boundaries between two successive zones asshown InFigu-res 2-5, inclusive, and to give the successive zones'the desired degrees of transparency. "It will beapparent that arcade the higher the degree of accuracy required, the smaller the step from one zone to another must be, and the greater the number of zones required for a given screen surface.

After the boundaries between adjacent zones have been calculated for any given function, the zones between them may be made of different transparency in any desired manner. For example, a suitable screen may be made from a photographic plate on which zones of different transparency are made by varying the time of exposure for the different zones. However, it is simpler and generally adequate to use a system of cross-etching, the density of which varies from one zone to another as shown in Figures 2-5, for example. In such case the light beam I2 in the apparatus shown in Figure 1 should not be too sharply focused, and it should cover sufiicient surface so that the amount of light transmitted through the screen l5 will truly represent the average transparency at that particular location.

For the functions z=xy (Figure 2) and (Figure 3) it has been assumed that the variables a: and 1/ have only positive values, and that the function has no negative values. For this reason, the origin of the :1:' 1/ coordinate system has been displaced away from the center of the screen so as to obtain a more efiicient use of its surface. Where this is done, the mirrors l5 and H should be adjusted so that the beam !2 in its initial position will lie on the origin of the screen I5.

It will be noted that in the case of the function z=x+y (Figure 4), both a: and y can be either positive or negative so that 2 can also be positive or negative. Thus, on the screen shown in Figure 4, the entire area above the diagonal line 38 represents positive values of 2, whereas the entire area below that line represents negative values at 2. For a function of this type, both positive and negative values may be obtained by employing two independently operating circuits like that of Figure 1 and by dividing the optical field into positive and negative sections. Such a solution is described in detail in connection with Figures 6 and 7.

The embodiment shown in Figure 6 is intended to be employed where a modulated light beam is used for the purpose of obtaining an alternating current output from a photoelectric cell. In this embodiment, the upper positive area of the screen l5, which may be of the type shown in Figure 4,- is isolated from the lower negative area thereof by means of an opaque screen 39, which is disposed perpendicularly to the screen 15 along the line 38.

Located on one side of the opaque screen 39 is the lens I6 and photoelectric cell H with its associated circuit. On the other side of the opaque screen 39 is disposed a second lens I6 and photoelectric cell l'l and its associated circuit. Since the circuit for the photoelectric cell [1 is identical with that for the photoelectric cell l1, corresponding parts in the former have been designated by corresponding primed reference characters. The output resistors 34 and 34 are connected in series by means of conductors 40, 4! and 42, such that the output at the terminals 43 and 44 is the difference between the voltages appearing across the resistors 34 and 34'.

If the value of the function a is positive so that the beam impinges upon the upper positive portion of the screen.l5, only -the photoelectric cell I! will be operative so that the voltage ap peering at the terminals 43 and 44 will be equal to the'voltage developed across the resistor 34. If, on the other hand, the value of the function 2 is negative so that the beam impinges upon the lower negative portion of the screen I5, only the photoelectric cell II will be energized, and the voltage at the terminals 43 and 44 will be substantially equal to the voltage developed across the resistor 34. This voltage will be equal in magnitude but opposite in polarity to the voltage developedlacross the resistor 34 when the value of the function e is positive and has the same absolute value.

' It will be apparent, therefore, that the circuit shown in Figure 6 provides outputs at the terminals 43 and 44 which have either positive or negative polarities depending upon whether the instantaneous values of the function 2 are p081 tive or negative.

If an unmcdulated light beam is employed, then the circuit shown in Figure 7 may be used. In this modification, the anodes i8 and I8 of the photoelectric cells I! and I1 should be connected together and to the positive terminal of a source of voltage 45, th negative terminal of which is connected to the'common point between two resistors 46 and 41. The other ends of the resistors 46 and 41 are connected to the oathodes I9 and IQ of the photoelectric cells I! and I1, thereby forming a Wheatstone bridge W1. The cathode [9 of the photoelectric cell I1 is also connected in series with a source of biasing voltage 48 to the control grid 49 of a conventional type electronic amplifying tube 50, the cathode 5| of which is connected to the cathode [9 of the photoelectric cell IT.

The plate circuit of the electronic tube 50 constitutes one of the arms of a second Wheatstone bridge W2; the other arms of which comprise the resistances 52, 53 and 54. A source of voltage 55 is connected to the cathode 5| of the tube 50 and to the mid-point between the resistors 52 and 53, and the output of the bridge W2 is provided at the terminals 56 and 51 which are connected to the plate electrode 58 of the tube 50 and the common point between the resistors 53 and 54, respectively.

In operation, both of the bridges are adjusted to be in balance when no light is falling upon the photoelectric cells I! and IT. The first bridge is balanced by changing the Value of one or both of the resistances 4B and 41; the second bridge is balanced by changing the value of resistance 54. If, however, light falls on either the photoelectric cell H or II, the second bridge W2, including the tube 50, is unbalanced providing an output at the terminals 56 and 51 which may be either positive or negative depending upon whether the light beam impinges upon the upper positive half of the screen l5 or the lower negative half thereof. In this embodiment, it is desirable to shield the optical system so as to prevent stray light from influencing the results obtained.

Similarly, the density screen can be arranged to give an output equal to the function a plus a, in which a is a positive constant sufficient to make e+a always positive. The output of the system would then give a potential difference corresponding to the z+a function and the quantity :1 can then be subtracted by means of a direct current potentiometer placed in series with the output to produce either a positive or negative funcion.

Thi ys em eih h ihs: he. as whe e he i heti h 3- a e ei h r os i e: heeet re an e 5 .39 l -inh epper tu es t iz ns wc rotating mirrors, but also with other apparatus hereinafterdescrihed.

Instead of usin m rr s ha ng; mu ual y nerpendicular axes of'rotation as shown in Figure 1-, e; cathode ray o l scope m e moleve as shown inFigure 8, for provldinga light beam that can be displaced in mutually perpendicular di ections in c da ce. th he a ues. If he variables a: and 11 Referring to F u e; a c vent n l. pe cathode ray oscilloscope is shown atC with its screen disposed adjacent the. screen. I5.- Theoseill s h C is ne g z d h-the-cen ent enalmaner from a source of. electrical energy. 59-,the.-DOS. itlvetermlnal of which. is groundedat 6.0.; The cathode 63 of the oscilloscope Qis connectedto the common point 64 between two resistors SJ and 62 connected across the voltage; source 59, and the accelerating electrodes 65 and. 5,6, are corrnected to the points 61. and, 60-, as Sho iin the figure. Negative bias, for the control grid 88 is provided. by connecting. itto the variable. contact 69 on the resistor BI.

The cathode. ray beam should preferably be modulated so as to. enable analter'nating current amplifier tobe usedwiththe photoelectric cell I]. To this end, alternating current is impressed upon the control grid: 68 from atransformer 10, the primary winding II of which is connected in the circuit of the control g id 68..

An electrical value proportional to the'variable is impressed upon the. terminals 12 and 13 which are connected to. the vertical deflecting plates '14 and 15, respectively, of. theoscilloscope C Comrected acrossthe terminals" and I3: is a resistance 15, the mid-step 1.1. ofwhlch ls con; net to r nd In sim lar ash a. v l a e p o io l h a ab s, mp e sedun h h m als 18 d 1, whi h er enne t d. o the horizontal deflecting plates 80. and 81, re.- spectively, of the oscilloscope C. A resistor 82 is connected across. the terminals. I8, andIB, the da of hi h is ne tedte ound The l escent spot. produce on e. c een of the cathode ray oscilloscope C by the cathode v bea in in he eenf rc idesa eem, of redielit e y hieh s itehsm tted h ush he screen l5 and is focused by the lens lfi uDQ the photoelectric cell L1. Since the latter. and its electrical circuit are identical with; the. corres. cone i al eeuihmen h i e e- 1, c r.- re p ence arac ers ha e enlu ed to designate corresponding partsthroughout,

Initially, the cathode ray oscilloscope Qis ad;- ius ed in the v n n mannehse h twheh the variables a: and y are.zero in magnitudathe cathode ray spot willlie atthe origin of the-ope ordinate system on the screen: I5. Electrical values directly proportional to instantaneous values of the variables at and yarethen impressed upon the vertical and horizontal deflecting plates, respectively, of the oscilloscope C; thereby causing the fluorescent spot to moveto corree spending positions on thescreen- I5. The light transmitted through the screen I5; at any given point corresponding to particular values of the variables a: and y is directly proportional tothe value of the function for those particular values i the ri b e e d iis he olte e me pressed across thereslstor 34 directly. HIQ-r portional to the instantaneous values of the tune;

ien. e or e pond g. .stenth-mee. value of the-variables x and 1!,

If; solutions are to be. made t functionshaving both positive and negative values, either of the circuits. shown in. Figures. 6. and '7 may be-substituted for the photoelectric cell. circuit shown in Figure 8, as described above.

Inthe embodiment shown in Figure 9 a televi-i sion tube of the type known as an iconoscope is employed for the purpose of solving for values ot a function of two variables. In this. figure, the, iconoscope is designatedby the reference character 84, and it is energized byv suitable sourcesof electrical energy 85, 86 and; 81 in the conventional manner. Light from a suitable Source isdirected through a screen I5- of the type, shown in Figures 2-5, inclusive, and. is f0;- cused' by means; of a, lens; I 6, upon. the photo:- sensitive screen. 89 of the iconoscope 8,4 sothat the light pattern on the photosensitivascreen." corresponds tothetransparency. of the screen I5, The light from the source 88, should; be; modulated, either by supplying alternating current to the source 88 or by interposing an interrupter G in the path of the beam, as shown in the figure.

Electrical values. proportional to the mag;- ni d s, h i e are; mpr ss pon he terminals 90 and SH which are connected to the vertical deflecting plates 92 and 93, respectively,- of the-iconoscope 84; In similar; fashion, electrical! values proportional to: the magnitudes-of the variable y are impressed upon the terminals 80 pdfit hich. are nnected o e o o tal. defleeting plates 96 and 91; respectively.- It will thusbe seen that the electronbemnprovidedby the electron gun- 98 will be displaced vertically in accordance with instantaneous values ofyand horizontally in accordancewith instantaneous values of m.

Init al he s i of h e nbeam s. ad uste s ha he h rz eb s. 1 ends. are o h er e em mp ne se he. origin of. the was, z/ y o din t s em of; e m se i h s reen. l5, form d. on the oto ens tive s re n.-

A'e n nin he-ar k he ntensity or the cur.- rent. flow ng; n.- th cir uit. of. the. photo-sensitive screen 89 varies with the intensity of them'odura edzlisht f in up n: hescreen at th -.poi t wheree t o beam impinges thereon. Accordingly, if instantaneous values of :r 811C111]: are applied to thevertical-deflecting plates 92; and 93 andthe horizontal plates, SIG-and 91, respectively; of the iconoscope 84; the current flowing in the circuit of the photosensitive element 89 will vary instantaneously in accordance. with the value of the function e, as determlned'bythe characteristics of the screen I5. This current is passed through a resistance 99 which is connected in series with a battery I00;

The voltage developed across the resistance-90 lsimpressed upon the control grid electrode IOI of'a conventional type electronic amplifying tube I02; in the plate circuit of \vhlch is connected the primary winding I03 of=a transformer I04; The secondarywinding I 95 of the transformer I is connected'to the anodes I06 and' I0! of conventional type rectifying tubes I08 and I09, respectively. The output of the rectifiers I08 and I09 is-irnpressed upon a load resistance IIO, one end Off'WhiCh is connected'to the mid-tap III of the transformer I04; and 'the other end of which is connected: to the-filaments H2 and H3 of the rectifying-tubes: I09 and I08; respectively; The voltageappearine atthe terminals I14 and H5;

respectively, will be directly proportional to incomplished in the embodiment shown in Figure 8 by modulating the voltage applied to the control grid 68 in accordance with the third variable. If the potential applied to the control grid 68 at each instant is such that the intensity of the electron beam is proportional to the function g(u) of the variable u and if, simultaneously, the electron beam is given a horizontal deflection proportional to the variable a: and a vertical deflection proportional to the variable y, the amount of light transmitted through the screen I at each instant will be proportional to the function z=g(u) -f(a:, y).

Solutions can also be obtained for more than three variables by using a plurality of solvers and utilizing the output of one to control the radiant energy beam of the second. For example, if a voltage proportional to the variable 11. is applied to the vertical deflection plates I4 and I5 of the cathode ray tube C in Figure 8, and a voltage proportional to the variable v is applied to the horizontal deflecting plates 80 and BI, the output of the photoelectric cell I! will be proportional to the function g(u, 1;). Similarly, if electrical values proportional to the variables y and a: are

applied to the horizontal and vertical deflecting plates of a second oscilloscope solver of the same type, the output of the photoelectric cell thereof will be proportional to the function f(m, y), assuming the intensity of the electron beam to be constant.

By applying the voltage which appears across the resistor 34, which voltage is proportional to the function g(u, v), to the control grid of the second oscilloscope, the intensity of the electron beam thereof will be proportional to the function gm, 1;), so that theoutput of the second solver will be proportional to the function z=g(u, v) 701:, y). j

The embodiment of the invention shown schematically in Figure utilizes a Farnsworth image disseotor tube. In this form of the invention, light from a source I passes through a screen I2I of the type shown in Figure 2 of the drawing, for example, and is focused by means of a lens I22 upon a photosensitive cathode I23 of the image dissector tube I24. The light intensity at any point on the cathode I23, therefore, corresponds to the transparency of the corresponding point on the screen I2 I.

The light from the source can be modulated either by supplying alternating current to the source I26 or by interposing an interruptor I25 between the light source I20 and the screen I2i. In, the Farnsworth tube, electrons are emitted from each point on the cathode I23 in proportion to the intensity of the light falling upon that point. Inasmuch as the light intensity at any point corresponds to the transparency of the screen IZI, the electron intensity at any point corresponds to the function' f(x, 1

The tube I24 includes an anode I26 to which a potential may be applied to attract the electrons emitted from the cathode I23. A focusing coil I2! within the tube produces a magnetic field coaxial with the tube. When the strength of the magnetic field is correctly adjusted, an electron. image of the cathode I23 is produced at a plane parallel to the cathode I23 and in the plane of the opening I28 in the tube member I29 which. projects into the tube I24. The electrons pass-. ing through the aperture I28 enter a series of electron multipliers I30 within the member I29. which increase the sensitivity of the tube.

The circuit connections to the anode, focusing. coil and electron multiplier are normal and fol.-.. low the manufacturers recommendations.

Outside the tube I24 are placed four coils I3I,. I32, I33 and I34. The coils I32 and I34 are con-.. nected in series in such a way that current passe, ing through them produces a uniform magnetic. field in a vertical direction. The coils I3I and I33 likewise are connected in series to produce a uniform horizontal field. The effect of these' magnetic fields is to change the direction of the electrons moving from the cathode I23 toward the anode I26 to the right or left and up and down. In this way, any part of the electron image. can be made to appear at the aperture I28.

Electrical values proportional to the magnitude of the variable :0 are impressed upon the ter-, minals I35 and I36 of the amplifier and current' control circuit I31 which is connected to the coils I32 and I34. The impressed electrical values will produce a current in the coils I32 and I34 causing a vertical magnetic field of the correct direction and strength to displace the electron image horizontally by an amount corresponding to the a: coordinate.

Similarly, electrical values proportional to the magnitude of the variable y are impressed upon the terminals I 38 and I39 of the amplifier and.

current control circuit I40 which is connected in series to the coils I 3| and I33. The horizontal, field produced will displace the electron image: vertically by an amount corresponding to the coordinate y.

Initially the circuits I31 and I40 are adjusted so that the part of the electron image corresponding to the origin of the xa:, y coordinate system of the image of the screen I2I formed on the'.

cathode I23 arrives at the aperture when both:

rectifier I42 like that described in connection with the iconoscope and disclosed in Figure 9. The voltage appearing at the output terminals I 43 and. I 44 will be directly proportional to the average instantaneous value of a.

While the use of the image dissector and the iconoscope have been described in connection with a screen of a type which gives only positive functions, it is possible to utilize these devices to deal with functions which can be either positive or negative. Thus, by illuminating a part of a screen with a light having one frequency and the other part of the screen with a light modulated to a different frequency and providing a filter before the output, the two frequencies can be separated to give two outputs which can be added algebraically, toproduce'an output which is either positive or negative.

- 'From the foregoing, it'will 'be apparent that solvers of the type described above may be employed for solving all types of functions of two variables and many types of functions of more than two variables. It will further be apparent that solvers constructed according to the invention include a minimum number of movingparts so that errors arising from inertia efiects and other mechanical "difliculties are reduced to a minimum. In those embodiments including a cathode ray oscilloscope or an iconoscope or an image 'dissector which utilizes an electron beam, inertia effects are completely eliminated, enabling solutions of desired functions to be obtained instantaneously.

'Solvers constructed according to the invention may be adapted for a wide variety of uses. For example, they may be employed in the solution of problems incident to gun fire control as well as in aircraft control systems "of the type disclosed in my copending application for Automatic control system for vehicles, filed July 1'7, 1943, Serial No. 495,093 now forfeited. Other uses will occur to those skilled in the art.

While several specific embodiments have been described above, the invention is not intended to be limited thereto. Those embodiments are susceptible to numerous changes in form and detail within the scope of the appended claims.

I claim:

1. An electrical solver for solving for values of a function of at least two variables comprising, means providing a beam of radiant energy, means for displacing said beam in different directions in proportion to the magnitudes of said respective variables, an optical screen in the path of said beam for modifying the intensity of said beam "in accordance with the instantaneous value of the function corresponding to the instantaneous values of the variables, said screen having one portion representing positive values of said function and another portion representing negative "values of said function, photosensitive means disposed to receive said modified beam, and electrical means connected to said photosensitive means for providing in a circuit an electrical value of one polarity proportional to positive values of said function, and an electrical value of different polarity proportional to negative values of said function.

2. An electrical solver for solving for values of a function of at least two variables comprising, means providing ab'eam of radiant energy, means for displacing said beam in different directions in proportion to the magnitudes of said respective variables, an optical screen in the path of said beam for modifying the intensity of said beam in accordance with the instantaneous value of the function corresponding to the instantaneous values of the variables, said screen having one portion representing positive values of said function and another portion representing nega tive values of said function, a plurality ofphotosensitive means disposed to receive'radiant energy from said portions of the optical screen, respectively, means for periodically varying the intensity of said beam, amplifying means for said respective photosensitive means, rectifying means connected to said amplifying means, means connecting the outputs of said rectifying means, in series opposition to electrically responsive means.

3. An electrical solver for solving for values of a function of at least two variables comprising, means providing a beam of radiant energy, means for displacing said beam in different directions in proportion to the magnitudes of said respective variables, an optical screen in the path of said beam for modifying the intensity of said beam'in accordance with the instantaneous value of the function corresponding to the instantaneous values of the variables, said screen having one portion representing positive values of said function and another portion representing negative values of said function, a plurality of photosensitive means disposed to receive radiant energy from said portions of the optical screen, respectively, an electrical network connected to said photosensitive means so as to constitute a Wheatstone bridge of which said photosensitive means constitute two adjacent arms, an electronic amplifying tube having control grid and cathode electrodes electrically connected to the output terminals of said Wheatstone bridge, a second electrical network connected in the plate-cathode circuit of said tube so as to constitute a second Wheatstone bridge of which said tube plate-cathode circuit comprises one of the arms, and means receiving the output of said second Wheatstone bridge.

HENRI-GEORGES DOLL.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES .PA'IENTS Number 7 Name Date 2,115,563 Tauschek Apr. 26, 1938 2,156,813 'Kautz May 2, 1939 2,199,066 Bernstein Apr. 30, 1940 2,243,600 Hulst, Jr. May 27, 1941 2,302,009 Dickinson Nov. 17, 1942 2,415,190 Rajchman Feb. 4, 1947 2,415,191 Rajchman Feb. 4, 1947 FOREIGN PATENTS Number Country Date 164,765 Great Britain June 23, 1921 OTHER REFERENCES Bedford: Figure of merit for television performance, RCA Review, July 1938.

Gray: A Photoelectric Integraph, publication of Mass. Inst. of Tech. EE. Dept. #73, Aug. 1931.

Awender-and Tombs: A curve tracer for two, three or four variables, Review of Scientific In struments,volume 8, Aug. 1937. 

